Mechanics knowledge catalogue

Engineering topics

Browse engineering mechanics and strength of materials topics with interactive practice problems for students and teachers.

• Theoretical Mechanics
  • Statics
    • Fundamentals of Forces and Moments
      • Basic Concepts of Statics. Force and Force Systems
      • Force Projections
      • Moment of a Force About a Point and an Axis
      • Force Couples and Couple Moment
      • Addition of Forces. Resultant of a Force System
      • Reduction of a Force System to a Given Point
    • Equilibrium of Coplanar Systems
      • Equilibrium Conditions for Coplanar Force Systems
      • Constraints and Constraint Reactions
      • Equilibrium of a Rigid Body in Two Dimensions
      • Equilibrium of Systems of Bodies. Method of Disassembly
      • Distributed Loads and Their Resultants
    • Three-Dimensional Statics
      • Three-Dimensional Force Systems
      • Equilibrium Conditions for Three-Dimensional Force Systems
      • Center of Parallel Forces and Center of Gravity
    • Friction
      • Sliding Friction. Coulomb's Laws
      • Equilibrium with Friction
      • Rolling Resistance
  • Kinematics
    • Particle Kinematics
      • Particle Kinematics. Methods of Describing Motion
      • Particle Velocity
      • Particle Acceleration
      • Special Cases of Particle Motion
    • Basic Motions of a Rigid Body
      • Translation of a Rigid Body
      • Rotation of a Rigid Body About a Fixed Axis
      • Velocities and Accelerations of Points in Fixed-Axis Rotation
      • Transmission of Rotational Motion
    • Plane Motion of a Rigid Body
      • Plane Motion of a Rigid Body
      • Velocities of Points in Plane Motion
      • Accelerations of Points in Plane Motion
    • Relative Motion of a Particle
      • Relative Motion of a Particle
      • Acceleration Addition. Coriolis Acceleration
    • Spatial Motion of a Rigid Body
      • Spherical Motion of a Rigid Body
      • General Motion of a Free Rigid Body
  • Dynamics
    • Particle Dynamics
      • Fundamental Laws of Dynamics. Newton's Laws
      • Differential Equations of Motion of a Particle
      • Two Fundamental Problems of Particle Dynamics
      • Particle Motion Under Typical Forces
    • General Theorems of Particle Dynamics
      • Linear Momentum of a Particle. Impulse of a Force
      • Angular Momentum of a Particle
      • Work of a Force. Power
      • Kinetic Energy of a Particle. Work-Energy Theorem
      • Potential Force Field. Potential Energy
      • Conservation of Mechanical Energy
    • Dynamics of Mechanical Systems
      • Dynamics of a Mechanical System. Center of Mass
      • Theorem on the Motion of the Center of Mass
      • Impulse-Momentum Theorem for a Mechanical System
      • Angular-Momentum Theorem for a Mechanical System
      • Kinetic Energy of a Mechanical System
      • Work-Energy Theorem for a Mechanical System
    • Analytical Mechanics and Oscillations
      • D'Alembert's Principle for a Particle and a System
      • Virtual Displacements. Principle of Virtual Work
      • General Equation of Dynamics
      • Lagrange's Equations of the Second Kind
      • Small Oscillations of a One-Degree-of-Freedom System
• Strength of Materials
  • Basic Concepts and Types of Deformation
    • Scope and Objectives of Strength of Materials
    • Deformation and Displacement
    • Elastic and Plastic Deformation
    • Basic Modes of Deformation
    • Strength, Stiffness and Stability
    • Basic Material Properties and Models
    • Composite Materials
    • Assumptions and Idealizations in Strength of Materials
    • Loads and Supports
    • Structural Element Models
    • External and Internal Forces. Method of Sections
    • Stress and Strain at a Point
  • Tension and Compression
    • Internal Forces and Stresses in Cross-Sections
    • Mechanical Properties of Materials
      • Tensile Test Diagram and Characteristic Points
      • Elastic Properties of Materials
      • Ductility and Brittleness of Materials
      • Allowable Stresses and Factor of Safety
      • Creep of Materials
      • Strain Hardening and Reloading
      • External Factors Affecting Mechanical Properties
    • Thermal Deformations and Stresses
    • Statically Indeterminate Problems under Axial Loading
    • Deformation of Bars in Tension and Compression
    • Strength and Stiffness Design in Tension and Compression
  • Shear and Direct Shear
    • Pure Shear and Design of Joints
  • Torsion
    • Internal Torque and Torque Diagrams
    • Torsion of Solid and Hollow Circular Shafts
    • Power Transmission by Shafts
    • Strength and Stiffness Design of Shafts
    • Statically Indeterminate Torsion
    • Design of Helical Springs
  • Stress and Strain State
    • Stress Analysis at a Point (Principal Stresses)
    • Strength Theories (Failure Criteria)
    • Generalized Hooke's Law
  • Geometric Properties of Plane Areas
    • Centroid and First Moments of Area
    • Second and Polar Moments of Area
    • Parallel-Axis Theorem and Composite Sections
    • Product of Inertia and Axis Rotation
    • Principal Axes, Principal Moments, and Section Moduli
  • Bending
    • Internal Forces in Bending
    • Stresses in Bending
    • Deflections in Bending
      • Differential Equation of the Elastic Curve
      • Initial Parameter Method (Macaulay's Method)
  • Combined Loading
    • Unsymmetrical Bending
    • Eccentric Compression
    • Combined Bending and Torsion
  • Energy Methods
    • Work of External Forces and Strain Energy
    • Castigliano's Theorem and Mohr's Integral
  • Stability of Compressed Members
    • Mechanism of Column Buckling
    • Column Buckling Modes
    • Column Slenderness and Weak Buckling Axis
    • Euler Buckling Formula and Critical Buckling Load
    • Critical Buckling Stress, Euler Limits and Inelastic Column Formulas
    • Column End Conditions and Effective Length
    • Column Stability Design Using Reduction Factor χ
    • Special Cases in Column Stability
    • Code-Based Design of Steel Compression Members
  • Shell Analysis
    • Membrane Theory
  • Dynamic and Cyclic Loading
    • Inertia Forces
    • Impact Loading Calculations
    • Material Fatigue and Endurance Limit
  • Contact Stresses
    • Contact of Two Bodies: Types and Geometry
    • Hertz Theory: Main Assumptions and Formulas
    • Contact of Spheres and Spherical Surfaces
    • Contact of Cylinders and Rollers
    • Stress State Beneath the Contact Surface
    • Contact Strength of Machine Elements
  • Torsion of Solid Noncircular Shafts
• Structural Mechanics
  • Fundamentals of Structural Mechanics
    • Structural Models and Idealization
    • Kinematic Analysis and Geometric Stability
    • Static Determinacy of Framed Structures
  • Statically Determinate Beams
    • Support Reactions and Internal Forces in Beams
    • Shear-Force and Bending-Moment Diagrams
    • Differential Relations between Load, Shear, and Moment
    • Hinged Multispan Beams
  • Statically Determinate Trusses
  • Statically Determinate Frames
  • Arches
    • Three-Hinged Arches
    • Internal Forces in Arches
    • Funicular Arch
  • Influence Lines
    • Influence Lines and Moving Loads
    • Influence Lines for Beam Support Reactions
    • Influence Lines for Shear and Bending Moment
    • Kinematic Method and Müller-Breslau Principle
    • Loading Influence Lines
    • Influence Lines in Hinged Multispan Beams
    • Influence Lines for Truss Member Forces
  • Displacements in Framed Structures
    • Work and Strain Energy
    • Mohr Integral and Unit-Load Method
    • Vereshchagin Rule
    • Displacements due to Temperature and Support Settlement
  • Force Method
    • Degree of Static Indeterminacy and Primary Structure
    • Canonical Equations of the Force Method
    • Beams and Frames by the Force Method
    • Temperature and Support Settlement in the Force Method
  • Displacement Method
    • Kinematic Indeterminacy and Primary System
    • Canonical Equations of the Displacement Method
    • Continuous Beams by the Displacement Method
    • Frames by the Displacement Method
  • Matrix Structural Analysis
    • Local Stiffness Matrix of a Structural Element
    • Coordinate Transformation and Global Element Stiffness
    • Assembly of the Global Equation System
    • Boundary Conditions, Displacements, and Force Recovery
• Machine Elements
  • Machine-Element Joints
    • Threaded Joints
      • Design of Interference-Fit Bolts
    • Riveted Joints
    • Welded Joints
    • Soldered and Adhesive Joints
    • Clamped Joints
    • Keyed and Splined Joints
    • Interference-Fit Joints
  • Mechanical Transmissions
    • Gear Drives
      • Worm Gear Drives
    • Strain-Wave Gear Drives
    • Friction Drives and Variators
    • Belt Drives
    • Chain Drives
    • Power Screws
  • Shafts and Axles
  • Bearings and Couplings
    • Plain Bearings
    • Rolling-Element Bearings
    • Couplings